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Associate Professor Bruce Van Brunt PhD

Associate Professor in Mathematics

Doctoral Supervisor
School of Mathematical and Computational Sciences

Professional

Qualifications

  • Doctor of Philosophy - University of Oxford (1990)

Research Projects

Completed Projects

Project Title: Lattice polytope samplers: theory, methods and applications

Date Range: 2018 - 2022

Funding Bodies: University of Otago; Royal Society of New Zealand

Project Team:

Research Outputs

Journal

Hazelton, M., McVeagh, M., Tuffley, C., & VAN BRUNT, B. (2024). Some rapidly mixing hit-and-run samplers for latent counts in linear inverse problems. Bernoulli. 30(4), 2676-2699
[Journal article]Authored by: Tuffley, C., Van Brunt, B.
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Mohsin, M., Zaidi, AA., & van Brunt, B. (2024). Dynamics of cell growth: Exponential growth and division after a minimum cell size. Partial Differential Equations in Applied Mathematics. 11
[Journal article]Authored by: Van Brunt, B.
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Derfel, G., & van Brunt, B. (2024). On the Balanced Pantograph Equation of Mixed Type. Ukrainian Mathematical Journal. 75(12), 1841-1849
[Journal article]Authored by: Van Brunt, B.
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Fatoyinbo, HO., Brown, RG., Simpson, DJW., & van Brunt, B. (2022). Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells. Bulletin of Mathematical Biology. 84(8)
[Journal article]Authored by: Brown, R., Simpson, D., Van Brunt, B.
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Zaidi, AA., & Van Brunt, B. (2021). Asymmetrical cell division with exponential growth. ANZIAM Journal. 63(1), 70-83
[Journal article]Authored by: Van Brunt, B.
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Hazelton, ML., Mcveagh, MR., & Van Brunt, B. (2021). Geometrically aware dynamic Markov bases for statistical linear inverse problems. Biometrika. 108(3), 609-626
[Journal article]Authored by: Van Brunt, B.
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Fatoyinbo, HO., Brown, RG., Simpson, DJW., & van Brunt, B. (2020). Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells. Bulletin of Mathematical Biology. 82(7)
[Journal article]Authored by: Brown, R., Simpson, D., Van Brunt, B.
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Lynch, TA., Wang, Y., van Brunt, B., Pacheco, D., & Janssen, PH. (2019). Modelling thermodynamic feedback on the metabolism of hydrogenotrophic methanogens. Journal of Theoretical Biology. 477, 14-23
[Journal article]Authored by: Lynch, T., Van Brunt, B.
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Efendiev, M., van Brunt, B., Zaidi, AA., & Shah, TH. (2018). Asymmetric cell division with stochastic growth rate. Dedicated to the memory of the late Spartak Agamirzayev. Mathematical Methods in the Applied Sciences. 41(17), 8059-8069
[Journal article]Authored by: Van Brunt, B.
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Van Brunt, B., Almalki, A., Lynch, T., & Zaidi, A. (2018). On a cell division equation with a linear growth rate. ANZIAM Journal. 59(3), 293-312
[Journal article]Authored by: Lynch, T., Van Brunt, B.
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Efendiev, M., van Brunt, B., Wake, GC., & Zaidi, AA. (2018). A functional partial differential equation arising in a cell growth model with dispersion. Mathematical Methods in the Applied Sciences. 41(4), 1541-1553
[Journal article]Authored by: Van Brunt, B.
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Wang, Y., Janssen, PH., Lynch, TA., Brunt, BV., & Pacheco, D. (2016). A mechanistic model of hydrogen-methanogen dynamics in the rumen. Journal of Theoretical Biology. 393, 75-81
[Journal article]Authored by: Lynch, T., Van Brunt, B.
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Van Brunt, B., Gul, S., & Wake, GC. (2015). A cell growth model adapted for the minimum cell size division. ANZIAM Journal : Electronic Supplement. 57(2), 138-149
[Journal article]Authored by: Van Brunt, B.
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Van Brunt, B., Wake, GC., & Zaidi, A. (2015). Probability density function solutions to a Bessel type pantograph equation. Applicable Analysis: an international journal. 95(11), 2565-2577
[Journal article]Authored by: Van Brunt, B.
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Zaidi, AA., Van Brunt, B., & Wake, GC. (2015). Solutions to an advanced functional partial differential equation of the pantograph type. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 471(2179)
[Journal article]Authored by: Van Brunt, B.
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Zaidi, AA., Van Brunt, B., & Wake, GC. (2015). A model for asymmetrical cell division. Mathematical Biosciences and Engineering. 12(3), 491-501
[Journal article]Authored by: Van Brunt, B.
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Derfel, G., van Brunt, B., & Wake, GC. (2012). A cell-growth model revisited. Journal of Functional Differential Equations. 19(1-2), 75-85
[Journal article]Authored by: Van Brunt, B.
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Van Brunt, B., & Vlieg-Hulstman, M. (2011). Eigenfunctions arising from a first-order functional differential equation in a cell growth model. ANZIAM Journal. 52(1), 46-58
[Journal article]Authored by: Van Brunt, B.
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Suebcharoen, T., Van Brunt, B., & Wake, GC. (2011). Asymmetric cell division in a size-structured growth model. Differential and Integral Equations. 24(7-8), 787-799
[Journal article]Authored by: Van Brunt, B.
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Van Brunt, B., & Wake, GC. (2011). A Mellin transform solution to a second-order pantograph equation with linear dispersion arising in a cell growth model. European Journal of Applied Mathematics. 22(2), 151-168
[Journal article]Authored by: Van Brunt, B.
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Van Brunt, B., & Vlieg-Hulstman, M. (2010). An eigenvalue problem involving a functional differential equation arising in a cell growth model. ANZIAM Journal. 51(4), 383-393
[Journal article]Authored by: Van Brunt, B.
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van Brunt, B., Kim, HO., & Derfel, G. (2010). Holomorphic solutions to functional differential equations. Journal of Mathematical Analysis and Applications. 368(1), 350-357
[Journal article]Authored by: Van Brunt, B.
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Senarath, P., Thornley, G., & Van Brunt, B. (2007). A system of PDES for Riemannian spaces. Journal of the Australian Mathematical Society. 82(2), 249-262
[Journal article]Authored by: Van Brunt, B.
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Van Brunt, B., & Vlieg Hulstman, M. (2008). Evolution equations having conservation laws with flux characteristics. ANZIAM Journal. 49(1), 39-52
[Journal article]Authored by: Van Brunt, B.
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Basse, B., Wake, GC., Wall, DJ., & Van Brunt, B. (2004). On a cell-growth model for plankton. Mathematical Medicine and Biology. 21, 49-61
[Journal article]Authored by: Van Brunt, B.
Basse, B., Wake, GC., Wall, DJN., & Van Brunt, B. (2004). On a cell-growth model for plankton. Mathematical Medicine and Biology. 21(1), 49-61
[Journal article]Authored by: Van Brunt, B.
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Basse, B., Baguley, BC., Marshall, ES., Joseph, WR., Van Brunt, B., Wake, G., . . . Wall, DJN. (2004). Modelling cell death in human tumour cell lines exposed to the anticancer drug paclitaxel. Journal of Mathematical Biology. 49(4), 329-357
[Journal article]Authored by: Van Brunt, B.
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Marshall, JC., van-Brunt, B., & Wake, GC. (2004). A natural boundary for solutions to the second order pantograph equation. Journal of Mathematical Analysis and Applications. 299(2), 314-321
[Journal article]Authored by: Marshall, J., Van Brunt, B.
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Van Brunt, B., Pidgeon, D., Vlieg-Hulstman, M., & Halford, WD. (2004). Conservation laws for second-order parabolic partial differential equations. ANZIAM Journal. 45(3), 333-348
[Journal article]Authored by: Van Brunt, B.
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van Brunt, B., Marshall, JC., & Wake, GC. (2004). Holomorphic solutions to pantograph type equations with neutral fixed points. Journal of Mathematical Analysis and Applications. 295(2), 557-569
[Journal article]Authored by: Marshall, J., Van Brunt, B.
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Van Brunt, B., Marshall, JC., & Wake, GC. (2003). An Eigenvalue problem for holomorphic solutions to a certain class of functional differential equations. European Journal of Applied Mathematics. 14(5), 571-585
[Journal article]Authored by: Marshall, J., Van Brunt, B.
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Basse, B., Baguley, BC., Marshall, ES., Joseph, WR., Van Brunt, B., Wake, G., . . . Wall, DJN. (2003). A mathematical model for analysis of the cell cycle in cell lines derived from human tumors. Journal of Mathematical Biology. 47(4), 295-312
[Journal article]Authored by: Van Brunt, B.
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Marshall, JC., Van Brunt, B., & Wake, GC. (2002). Natural boundaries for solutions to a certain class of functional differential equations. Journal of Mathematical Analysis and Applications. 268(1), 157-170
[Journal article]Authored by: Marshall, J., Van Brunt, B.
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Van Brunt, B., Wake, GC., & Kim, HK. (2001). On a singular Sturm-Liouville problem involving an advanced functional differential equation. European Journal of Applied Mathematics. 12(6), 625-644
[Journal article]Authored by: Van Brunt, B.
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Wiles, PG., & Van Brunt, B. (2001). Optimal location of transshipment depots. Transportation Research Part A: Policy and Practice. 35(8), 745-771
[Journal article]Authored by: Van Brunt, B.
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Selvaratnam, AR., Vlieg-Hulstman, M., Van-Brunt, B., & Halford, WD. (2001). On the solution of a class of second-order quasi-linear pdes and the gauss equation. ANZIAM Journal. 42(3), 312-323
[Journal article]Authored by: Van Brunt, B.
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Wake, GC., Cooper, S., Kim, H., & Van Brunt, B. (2000). Functional differential equations for cell-growth models with dispersion. Communications in Applied Analysis. 4(4), 561-573
[Journal article]Authored by: Cooper, S., Van Brunt, B.
Milliken, P., Marsh, C., & van Brunt, B. (1999). Minimax controller design for a class of uncertain linear systems. Automatica. 35(4), 583-590
[Journal article]Authored by: Van Brunt, B.
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Van-Brunt, B., & Grant, K. (1996). Potential applications of Weingarten surfaces in CAGD, part I: Weingarten surfaces and surface shape investigation. Computer Aided Geometric Design. 13(6), 569-582
[Journal article]Authored by: Van Brunt, B.
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Van-Brunt, B., & Grant, K. (1994). Hyperbolic Weingarten surfaces. Mathematical Proceedings of the Cambridge Philosophical Society. 116(3), 489-504
[Journal article]Authored by: Van Brunt, B.
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Van-Brunt, B. (1994). Mathematical possibility of certain systems in geometrical optics. Journal of the Optical Society of America A: Optics and Image Science, and Vision. 11(11), 2905-2914
[Journal article]Authored by: Van Brunt, B.
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van-Brunt, B., & Ockendon, JR. (1992). A lens focusing light at two different wavelengths. Journal of Mathematical Analysis and Applications. 165(1), 156-179
[Journal article]Authored by: Van Brunt, B.
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Book

Little, CH., Teo, K., & Van Brunt, B.(2003). The number systems of analysis. River Edge, NJ: World Scientific
[Authored Book]Authored by: Van Brunt, B.

Conference

Fatoyinbo, HO., Brown, RG., Simpson, DJW., & Van Brunt, B. (2022). EFFECTS OF CONDUCTANCE OF ION CHANNELS ON SPONTANEOUS ELECTRICAL ACTIVITY IN SMOOTH MUSCLES. , 13th INTERNATIONAL CONFERENCE DYNAMICAL SYSTEMS APPLIED TO BIOLOGY AND NATURAL SCIENCES (DSABNS)
[Conference Abstract]Authored by: Simpson, D., Van Brunt, B.
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Doumic, M., & Van Brunt, B. (2018). Explicit Solution and Fine Asymptotics for a Critical Growth-Fragmentation Equation. In P. Gabriel, L. Dumas, M. Dauhoo, & P. Lafitte (Eds.) ESAIM: PROCEEDINGS AND SURVEYS. Vol. 62 (pp. 30 - 42). : CIMPA School on Mathematical Models in Biology and Medicine
[Conference Paper in Published Proceedings]Authored by: Van Brunt, B.
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Lynch, T., Van Brunt, B., & Zaidi, AA. (2018). CELL DIVISION AND THE PANTOGRAPH EQUATION. ESAIM: PROCEEDINGS AND SURVEYS. Vol. 62 (pp. 158 - 167).
[Conference Paper in Published Proceedings]Authored by: Lynch, T., Van Brunt, B.
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Van Brunt, B. (2017, March). Analytical solutions to certain equations from a cell division equation. Presented at Workshop on: Coagulation and Fragmentation Equations. Vienna, Austria.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2016, December). On a simple model for size structured asymmetric cell division. Presented at CIMPA 2016 Research School Mathematical Models in Biology and Medicine. Mauritius, East Africa.
[Conference Oral Presentation]Authored by: Van Brunt, B.

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Van Brunt, B. (2016, July). Exact solutions and higher order asymptotics for a cell division equation. Presented at 10th European Conference on Mathematical and Theoretical Biology. Nottingham, United Kingdom.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2016, May). Exact Solutions and higher order asymptotics for a cell division equation. Presented at International Conference on Differential Equations and Applications. Lahore University of Management Sciences, Lahore, Pakistan.
[Conference Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B., Zaidi, A., & Wake, G. (2015, November). A Second Order Initial Boundary Value Problem for Cell Growth. Presented at New Zealand Mathematical Colloquium 2015. Christchurch, New Zealand.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2015, May). Higher order asymptotics of solutions to initial-boundary value problems involving a functional argument. Presented at Differential equations with variable delay. Toronto, Canada.
[Conference Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B., Gul, S., & Wake, GC.A CELL GROWTH MODEL ADAPTED FOR THE MINIMUM CELL SIZE DIVISION.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B., Wake, G., & Zaidi, A. (2014, December). On the solution to a nonlocal PDE from a cell growth model. Presented at 8th Australia-New Zealand Mathematics Convention. Melbourne, Australia.
[Conference Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B. (2014, February). An initial-boundary value problem arising in a fragmentation/cell division model. Presented at ANZIAM. Rotorua, New Zealand.
[Conference Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B. (2013, December). Eigenfunction expansions for solutions to a nonlocal PDE from a cell growth model. Presented at New Zealand Mathematics Colloquium. Tauranga, New Zealand.
[Conference Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B., Wake, G., & Zaidi, A. (2014). Tumour cell biology and some new non-local calculus. In M. Wakayama, R. McKibbin, R. Anderssen, J. Cheng, K. Polthier, & K. Toh (Eds.) The Impact of Applications on Mathematics: Proceedings of the Forum lf Mathematics for Industry. Vol. 1 (pp. 27 - 33). Japan: Mathematics for Industry
[Conference Paper in Published Proceedings]Authored by: Van Brunt, B.
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Van Brunt, B. (2012, December). An initial-boundary value problem arising in a fragmentation/cell division model. Presented at New Zealand Mathematics Colloquium. 黑料网, Palmerston North.
[Conference Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B. (2011, November). Eigenfunctions from a cell growth model. Presented at 14th Manawatu-Wellington Applied Mathematics Meeting. Industrial Research, Wellington.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Zaidi, AA., van-Brunt, B., & Wake, GC.Probability density function solutions to a Bessel type pantograph equation.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2010, June). The Pantograph Equation. Presented at Industrial Mathematics Intiative 2010. KAIST, Daejeon South Korea.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2010, April). Conservation Laws and Characteristics for Certain Classes of Evolution Equations. Presented at KAIST-NIMS International Workshop on Nonlinear Partial Differential Equations: theory, application and numerical computing. Daejeon, South Korea.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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van Brunt, B., & Wake, G. (2010, January). A Pantograph equation with nonconstant dispersion. . Queenstown New Zealand.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2010, December). A singular Sturm-Liouville problem arising from a cell growth model. Presented at New Zealand Mathematical Society Colloquium 2010. Dunedin.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2008, December). Holomorphic solutions for a class of functional differential equations. Presented at 7th Joint Australia-New Zealand Mathematics Convention 2008. Christchurch New Zealand.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B., & Marshall, JC. (2005). Holomorphic solutions to linear first-order functional differential equations. Electronic Journal of Differential Equations. Vol. 12 (pp. 39 - 46). San Marcos, TX: 2004 Conference on Differential Equations and Applications in Mathematical Biology
[Conference Paper in Published Proceedings]Authored by: Van Brunt, B.
Milliken, P., Marsh, C., & van Brunt, B.Controller synthesis for robust performance using H <inf>∞</inf> with transients for structured uncertainty. Proceedings of the IEEE Conference on Decision and Control. (pp. 2828 - 2829). 0191-2216.
[Conference]Authored by: Van Brunt, B.
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Milliken, P., Marsh, C., & van Brunt, B.(1997, June). State feedback minimax and guaranteed cost controllers for linear systems with integral quadratic constraint uncertainty descriptions. ROBUST CONTROL DESIGN (ROCODN'97). (pp. 347 - 352).
[Conference]Authored by: Van Brunt, B.

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Other

Van Brunt, B. (2016, July). On a functional differential equation arising in a cell division model. In Mathematics Department, Munich Technical University, Munich Germany.
[Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2016, March). On a second order initial boundary value problem that models cell division. In Math colloquium. Presented at Ben Gurion University, Beer Sheva Israel.
[Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B., Little, C., & Teo, K. (2015). Real Analysis via Sequences and Series. Springer Verlag
[Other]Authored by: Van Brunt, B.
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Van Brunt, B. (2012, September). Functional Equations, Star Wars, Cell Growth. In General Talk, 黑料网.
[Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B. (2004). The Calculus of Variations. Springer Verlag
[Other]Authored by: Van Brunt, B.
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Van Brunt, B., Little, C., & Teo, K. (2003). Number Systems of Analysis. World Scientific
[Other]Authored by: Van Brunt, B.
Van Brunt, B., & Carter, M. (2000). The Lebesgue-Stieltjes Integral. Springer Verlag
[Other]Authored by: Van Brunt, B.
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Teaching and Supervision

Contact Supervisor

Summary of Doctoral Supervision

Position Current Completed
Main Supervisor 0 5
Co-supervisor 1 4

Current Doctoral Supervision

Co-supervisor of:

  • Brandon Jones - Doctor of Philosophy
    Mathematical modelling of growth and metabolism in complex microbial communities

Completed Doctoral Supervision

Main Supervisor of:

  • 2021 - Michael McVeagh - Doctor of Philosophy
    Efficient Markov bases for Z-polytope sampling
  • 2021 - Hammed Fatoyinbo - Doctor of Philosophy
    Pattern Formation in Electrically Coupled Pacemaker Cells
  • 2020 - Adel Almalki - Doctor of Philosophy
    The Analysis of Fragmentation Type Equations for Special Division Kernels
  • 2019 - Saima Gul - Doctor of Philosophy
    Differential equations arising in the study of a cell growth model
  • 2006 - Jonathan Marshall - Doctor of Philosophy
    Holomorphic Solutions to Functional Differential Equations

Co-supervisor of:

  • 2017 - Yuancheng Wang - Doctor of Philosophy
    Mechanistic modelling of enteric methane production
  • 2015 - Ali Ashher Zaidi - Doctor of Philosophy
    Mathematics of Cell Growth
  • 2013 - Fleur McDonald - Doctor of Philosophy
    Travelling Wave Solutions of Multisymplectic Discretisations of Wave Equations
  • 2000 - Paul Milliken - Doctor of Philosophy
    Minimax approaches to Robust Control.